1. Field of the Invention
The present invention relates to a numerical calculation technology which is used for obtaining an approximate solution of a differential equation.
2. Background Art
Fluid calculation is necessary for state estimation of an intake system and a hydraulic system of an internal combustion engine. At present, in the field of an arithmetic method for the fluid calculation, a large number of inventions relating to a method of solving a partial differential equation of a distributed parameter system have been made. For example, JP Patent Publication (Kokai) No. 2008-197949 A discloses a technique of enhancing calculation accuracy according to a local interpolation differential operator method. More specifically, JP Patent Publication (Kokai) No. 2008-197949 A discloses a technique of time-integrating a variable by applying semi-Lagrangian advection in which the Lagrangian method is applied to an advection term, to an advection term of a partial differential equation for an interpolation function regarding the variable to be time-integrated.
JP Patent Publication (Kokai) No. 2008-197949 A relates to a numerical calculation technique for stably solving a partial differential equation expressed in Expression (1).
                    [                  Expression          ⁢                                          ⁢          1                ]                                                                                                ∂              f                                      ∂              t                                +                                    ∂              uf                                      ∂              x                                      =        0                            (        1        )            
This differential equation is often used for calculation of a one-dimensional fluid. In this equation, f represents the density and u represents the speed. In order to stably solve Expression (1), the following two conditions are required.    (Condition 1) Smoothing of partial differential for obtaining ∂uf/∂x with excellent accuracy    (Condition 2) Stabilization of integral of −∂uf/∂x for a time point t for obtaining f with excellent accuracy
The technique disclosed in JP Patent Publication (Kokai) No. 2008-197949 A relates to (Condition 1), and (Condition 2) has not been satisfied yet.